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arXiv · 0903.0449

Coupled paraxial wave equations in random media in the white-noise regime

Josselin Garnier·Knut Sølna
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Abstract

In this paper the reflection and transmission of waves by a three-dimensional random medium are studied in a white-noise and paraxial regime. The limit system derives from the acoustic wave equations and is described by a coupled system of random Schrödinger equations driven by a Brownian field whose covariance is determined by the two-point statistics of the fluctuations of the random medium. For the reflected and transmitted fields the associated Wigner distributions and the autocorrelation functions are determined by a closed system of transport equations. The Wigner distribution is then used to describe the enhanced backscattering phenomenon for the reflected field.

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Josselin Garnier, Knut Sølna. 2009-03-03. Coupled paraxial wave equations in random media in the white-noise regime. https://doi.org/10.1214/08-aap543

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